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comment Why is that *any* union of open sets is open but only *finitely many* intersections of open sets is open?
Topology really began from the study of the real line, and then realising that similar approaches work in various "spaces". Since in the real line the family of open sets is closed under arbitrary unions, finite intersections, but not necessarily infinite intersections, it makes sense that the definition of a topology only demands that the family of open sets be closed under finite intersections. There are classes of topological spaces that a closed under longer intersections: for example, in a P-space the family of open sets is closed under countable intersections.
1d
answered Why $C$ is a null set which is not a strong measure zero set?
Aug
17
comment union(new: intersection) of any number of open sets is also open
This question appears to be off-topic because it no longer has any content since the link to the image is dead.
Aug
17
answered Countably local finiteness and a related(?) property
Aug
10
awarded  Good Answer
Aug
1
revised Limits of the joint pdf $(2/3)(x + 2y)$
tried to improve.
Aug
1
revised Can every uncountable subset of $\mathbb R$ be split up this way?
deleted 27 characters in body
Aug
1
answered Can every uncountable subset of $\mathbb R$ be split up this way?
Aug
1
revised Expected maximum score(dice).
mod note
Aug
1
revised Expected probablility in dice tossing
added 25 characters in body
Aug
1
revised Expected probablility in dice tossing
added 25 characters in body
Aug
1
revised Expected probablility in dice tossing
added 25 characters in body
Aug
1
revised Expected probablility in dice tossing
moderator ntoe
Aug
1
revised Count arrangment such that each person wear different tshirt
moderator note
Aug
1
revised Cleaning minimum tables
moderator note
Aug
1
revised Find if person go through given point
moderator note
Aug
1
revised ${\bf E}[Y]$ of a joint distribution
improved?
Aug
1
revised The probability that a joint distribution is less than a certain value, given the correlation coefficient.
improved?
Aug
1
revised The product of three consecutive natural numbers is divisible by $6$
improved.
Aug
1
comment The set of rational numbers, each point is point accumulation
@Semiclassical: There is no need to remove the (homework) tag when others exist. The burnination process will remove the tag automatically in a few days. In fact, unless you are making other edits to the post, it is much preferred to leave it alone, since there's enough bumping going on these days to fix the posts that actually do need fixing.